A driven system has the following measured (driving frequency in Hz, steady amplitude in mm) pairs: (1, 1), (1.5, 3), (2, 8), (2.5, 4), (3, 2). The driving-force amplitude was kept constant. Identify all sampled frequencies with the largest response, calculate the ratio of largest amplitude to the amplitude at 1 Hz, and assess whether the measurements locate one exact resonant frequency. Propose a next measurement range and one reliability check.

Question

Accepted Answer

Largest measured amplitude 8 mm at 2 Hz; amplitude ratio 8. The sampled maximum locates a candidate region, not an exact continuous peak. Compare the measured amplitudes rather than choosing the largest frequency. The greatest recorded amplitude is 8 mm at 2 Hz; the final sampled amplitude is 2 mm. The requested comparison is an amplitude ratio: 8/1 = 8. It has no unit and is not automatically an energy ratio, because the question supplies amplitude measurements only. Sample more densely on both sides of the largest recorded response, because a narrower maximum may lie between the original frequency settings. A resonance interpretation requires the system to receive the same driving-force amplitude at each frequency and enough time to settle. Repeat the scan in both directions to check for drift, history effects and inconsistent settling. Report the observed response pattern with its sampling limitation. A single scan cannot prove one exact natural frequency, establish damping quantitatively or exclude multiple modes; those claims require additional measurements and an appropriate model.

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What a complete response should do

Measured driven response

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Measured driven response — supplied values
Driving frequency (Hz)	Amplitude (mm)
1	1
1.5	3
2	8
2.5	4
3	2